$A$ metal sphere of mass $m$ and density $\sigma_1$ falls with terminal velocity through a container containing liquid. The density of the liquid is $\sigma_2$. The viscous force acting on the sphere is:

• A
  $m g\left(1+\frac{\sigma_2}{\sigma_1}\right)$
• B
  $m g\left(1-\frac{\sigma_1}{\sigma_2}\right)$
• C
  $m g\left(1-\frac{\sigma_2}{\sigma_1}\right)$
• D
  $m g\left(1+\frac{\sigma_1}{\sigma_2}\right)$